Question

27. If A=B=60º, verify that
(1) cos (A - B) = cos A cos B + sin A sin B
(ii) sin (A - B) = sin A cos B - cos A sin B
(iii) tan (A - B) = tan A - tan B / 1 + tan A tan B​

Answer 1

Given A=B=60∘

cos(A−B)=cos(0)=1.

Now, cosAcosB+sinAsinB=cos(60∘)cos(60∘)+sin(60∘)sin(60∘)

=>34+14=44=1

henc proved.

Second Part,

tan(A−B)=tanA−tanB1+tanAtanB

tan(A−B)=tan(60−60)=tan0=0 =>tanA−tanB1+tanAtanB=tan(60∘)−tan(60∘)1+tan(60∘)tan(60∘)=0.

Hence Proved.